Question
If 91, 326, 147, 271, 193, 371, 416 is the second step
of an input, which of the following steps will be 91, 147, 193, 271, 326, 371, 416? Directions: A number arrange machine, when given a particular input, rearranges it following a particular rule. The following is the illustration of the input and the steps of arrangement: Input: 207, 59, 324, 23, 135, 173, 312 Step I: 207, 59, 312, 23, 135, 173, 324 Step II: 23, 59, 312, 207, 135, 173, 324 Step III: 23, 59, 173, 207, 135, 312, 324 Step IV: 23, 59, 135, 207, 173, 312, 324 Step V: 23, 59, 135, 173, 207, 312, 324 This is the final arrangement and step V is the last step for this input.Solution
Here the rule followed is: Numbers are getting arranged in ascending order. The largest no. interchanges with the last-position no. Then the smallest no. interchanges with the first-position no. Next, the second largest no. interchanges with the second last position no. And so on.[Note: In step IV it is clear that when second smallest no.. is already set, the no. just larger to it interchanges with the next no.. From this it is clear that in odd step we should deal with larger no. and in even step we should deal with smaller no.] Step II: 91, 326, 147, 271, 193, 371, 416 Step III: 91, 193, 147, 271, 326, 371, 416 Step IV: 91, 147, 193, 271, 326, 371, 416
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